The mechanisms of dissemination of the counting frames in the teaching of mathematics in Spain during the nineteenth century are studied. José Mariano Vallejo and Pablo Montesino proposed them in order to facilitate an arithmetic initiation based on intuition, following Pestalozzi's proposals. The diffusion channels considered were pedagogical…

Discusses mental computation and how and when it should be taught. Describes seven properties of mental algorithms. (YP)

Students who can compute mathematical problems in their heads have learned a skill that is important for estimating and for understanding the number system. Practice activities that can help students master mental computation skills are described. (PP)

A range of estimation techniques are described, and a series of mental computation procedures based on concepts of measurement and real numbers are presented in detail. (MP)

The relationship between automatization ability (the tendency for repetitive routine aspects of behavior to become so overlearned that a minimum of conscious effort and attention is necessary for rapid efficient execution), as measured by the Rapid Automatic Naming (RAN) Test, and proficiency in arithmetic basic fact computation was investigated…

Presented is a method of teaching adding and subtracting as an interrelated series of patterns using a number line. Examples of the use of this method as well as the materials necessary are discussed. Applications of the method to multiplication and division are given. (CW)

Suggests that algorithms, both traditional and student-invented, are proper objects of study not only as tools for computation, but also for understanding the nature of the operations of arithmetic. (Author/NB)

Describes the work that students and teachers do to develop computational fluency for subtraction. Examines the orchestration of whole-class discourse and presents a collection of common strategies. (Author/NB)

Suggests ways to increase students' computational fluency using concrete materials, engaging tasks, and reflection time to increase number automaticity, flexibility in thinking about numbers, and use of efficient problem-solving strategies to find sums and differences. (Author/NB)

Uses interviews with 72 pupils in grades 2-6 to investigate awareness of the relation between situation and computation in simple quotitive and partitive division problems as informally and formally experienced. Concludes that formal division, understood as related to everyday situations, only depends in interplay with informal knowledge.…

Teacher planning procedures employing percentage-based measurement summaries and subsequent implementation of the results of planning with and without error analysis resulted in moderate increases in correct mathematics computation of learning disabled 10-13 year olds. No significant differences were found for presence or absence of error…

Provides an alternative to traditional instruction in multiplication and division to develop computational fluency in students. (Author/NB)

Presents math games with die designed to help students learn addition, subtraction, and multiplication while having fun. (KHR)

The study involving 183 learning disabled and 852 nondisabled children (grades 3 through 6), investigated students' performance on arithmetic basic fact problems in addition, subtraction, and multiplication. Three separate group administered tests were devised, covering 98 basic addition, 98 subtraction, and 98 multiplication facts. Children were…

Six easy-to-learn strategies are offered to help students with learning problems in mathematics make error-free subtraction calculations when either the subtrahend or remainder is a 9, 8, or 7 and when the minuend is in the teens. (CB)